I am excited to see that Stan is beginning to provide support for complex numbers. I am interested in using Stan for a quantum model, but this requires additional features. I was wondering whether Stan will support matrix_exp and user defined functions with complex number support in the future. If so, is there an approximate timeline? Thank you.

I would not be so sure about supporting the matrix exponentialâ€¦itâ€™s certainly a great thing. So maybe search for complex number support for different operations on GitHub. Or is the implementation for complex numbers so general such that the matrix_exp function as currently implemented will â€śjust workâ€ť? @Bob_Carpenter ? I would think that it needs adjustments to be able to deal with complex numbers, right?

tiny demo with debian stable clang-11 & libeigen3-dev

#include <Eigen/Dense>
#include <unsupported/Eigen/MatrixFunctions>
#include <complex>
#include <iostream>
using namespace std::literals;
int main()
{
Eigen::MatrixXcd a(2,2);
a << 1.0 + 2.0i, 2.0 + 1.0i, 3.0 - 1.0i, 4.0 - 2.0i;
std::cout << "The matrix A is:\n" << a << "\n\n";
std::cout << "The matrix exponential of A is:\n" << a.exp() << "\n\n";
}

$ clang++-11 -I /usr/include/eigen3/ main.cpp -o main
$ ./main
The matrix A is:
(1,2) (2,1)
(3,-1) (4,-2)
The matrix exponential of A is:
(39.1276,7.06055) (60.9904,-9.96502)
(51.0254,-70.9555) (41.6007,-131.104)

Still a decision for Stan developers to decide how easy it would be to maintain â€“ e.g. if Stan adds support for complex matrix exponential, this might be relatively simple to do for code that executes with an eigen backend but may be hard to do for other backends (e.g. would it need to be hand implemented for CUDA ? ).

My understanding is that as long as we have one working definition in /prim, the other folders are all optional (theyâ€™ll be used if they exist, but if they donâ€™t it falls back to the prim implementation)